Arc Length Calculator

Arc length calculator calculates the length of an arc by knowing its radius or diameter, area, or central angle.

Arc Length Formula

By knowing the radius and angle for an acr, the arc length formula is

L = 2πr(θ/360°)
where
r = radius of the circle.
θ = degrees.

Or

L = θr
where θ = radians.

The arc length formula is derived from the perimeter of the circle.
As we know, the perimeter of the circle is:
p = 2πr

Consider an arc as a sector of a circle and one circle is 360 degrees, to calculate this sector of a circle, we divide the sector's degree by 360 which is θ/360.

Therefore, we get the formula:
L = 2πr(θ/360°)

If the central angle θ is in radians, we need to replace degrees with radians.
Degrees = Radians x 180 /π

With the replacement of degrees, we will get:
L = 2πr(Radians x 180 /π /360°)

Simplify it:
L = θr
where θ = radians

More Arc Length Formula

There are more derived formulas for arc length.

L = A / r x 2.
where A = area of the arc.
r = radius of the arc.

L=θ √A x 2 / θ
where A = area of the arc
θ = the central angle in radians.